Central limit theorem and almost sure results for the empirical estimator of superquantiles/CVaR in the stationary case

Jérôme Dedecker (1) , Florence Merlevède (2)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 LAMA - Laboratoire Analyse et de Mathématiques Appliquées

In this paper, we show that the difference between the empirical estimator and the Conditional value-at-risk can be written as a simple partial sum + a residual term. Starting from this decomposition, we prove a central limit theorem and some almost sure results for the empirical estimator, for a large class of stationary sequences. We also construct a confidence interval with asymptotic level 1 − α, and we study its coverage level through two different sets of simulation.

Mots clés: Average value-at-risk; Conditional value-at-risk; Expected shortfall; Superquantiles; Stationary sequences; Mixing sequences

Domaines: Statistiques [stat]

Jérôme Dedecker, Florence Merlevède. Central limit theorem and almost sure results for the empirical estimator of superquantiles/CVaR in the stationary case. Statistics, 2022, 56 (1), pp.53-72. ⟨10.1080/02331888.2022.2043325⟩. ⟨hal-03214790⟩